The sound field of harmonically radiating point sources moving along arbitrary trajectories in one, two and three dimensions is studied in the frequency domain. First, we analyze sources moving rectilinearly with constant velocity over an infinite time interval. Then, the method is generalized threefold by taking into account arbitrary trajectories, introducing dampingDamping effects, and considering finite observation times of the source’s motion. The so-called “Cartesian convolution integralCartesian convolution integral” is derived and applied to sources that can move on generally formulated trajectories, such as circular, conical and elliptical helices. For purely circular trajectoriesCircular trajectories and helical orbitsHelical orbits, an alternative approach in cylindrical or spherical coordinates leads to closed-form expressions in the form of infinite series for the frequency spectra. Comparing the results of the Cartesian convolution integral with those of the series expansion shows excellent agreement. We also investigate moving sources above an impedance planeImpedance plane in one, two, and three dimensions. Finally, we study the frequency spectrum of “real sources” with a finite, non-zero volume based on the Ffowcs Williams and Hawkings equationFfowcs Williams and Hawkings equation. For this reason, we derive a frequency domain formulation of the Ffowcs Williams and Hawkings equation.